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At least 20 killed by suspected ISIS bombings in Iraq

Iraq's special forces worked on Sunday to fully clear neighbourhoods on Mosul's eastern edge of ISIS militants, as bombings killed at least 20 people elsewhere around the country.

The current phase and slower pace highlight the challenges ahead for Iraqi forces as they press into more populated areas deeper inside Mosul, where the civilian presence means they won't be able to rely as much on airstrikes.

"There are a lot of civilians and we are trying to protect them," said Lt Col Muhanad al-Timimi.

"This is one of the hardest battles that we've faced till now."

Some civilians are fleeing the combat zone, while ISIS militants are holding others back for use as human shields, making it harder for Iraqi commanders on the ground to get approval for requests for US-led coalition air strikes.

Iraqi special forces near Hammam Al-Alil. (AAP)

Iraq's special forces are some of the country's best troops, but they still largely rely on air support to clear terrain.

Iraqi forces first entered the eastern edge of the city on Tuesday. On Friday, forces began pushing into Mosul proper, but so far have only advanced just over a kilometre into the city.

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On the city's southern front Iraqi forces are still some 20km from the city centre.

The extremists captured the city in 2014, and have had plenty of time to erect fortifications.

Men are held by Iraqi national security agents, to be interrogated at a checkpoint, as oil fields burn in Qayara, south of Mosul. (AAP)

Trenches and berms have turned the streets and alleyways of a neighbourhood once named after former Iraqi leader Saddam Hussein into a maze, and concrete blast walls have blocked off access to other areas.

"Daesh dug trenches that they filled with water and they have a lot of suicide attackers and car bombs," said al-Timimi, using the Arabic acronym for ISIS.

ISIS fought back Saturday, pushing the special forces from the southern edge of the Gogjali neighbourhood, where the troops had made their first major foray into the city itself after more than two weeks of fighting in its rural outskirts.

Both sides fired mortar rounds and automatic weapons, while the Iraqi troops also responded with artillery.

Snipers duelled from rooftops in residential areas, where most buildings are just two storeys high.

Meanwhile suspected ISIS militants struck far from the front lines with a pair of bombings that killed at least 20 people.

One suicide attack against Shi'Ite pilgrims north of Baghdad killed at least 11 people.